UK police chiefs have reacted sceptically to plans for US "supercop" Bill Bratton to advise the government.
David Cameron has called for the former New York police chief to help address violence in English cities.
Association of Chief Police Officers' head Sir Hugh Orde said: "I am not sure I want to learn about gangs from an area of America that has 400 of them."
There have been no reports of unrest this weekend, as extra police numbers have been maintained on city streets.
Weekend court sittings are continuing to hear the cases of more than 1,000 people charged since violence flared last weekend.
Among those appearing before Birmingham magistrates were Joshua Donald, 26, and a 17-year-old boy who are charged with the murders of three men hit by a car during disruption in the city.
The pair were remanded to appear in Birmingham Crown Court on Monday.
Meanwhile, a peace rally is being held on Sunday afternoon in Winson Green, the neighbourhood where the men were killed. Up to 20,000 people are expected to attend.
Sir Hugh, president of the Association of Chief Police Officers (Acpo), questioned Mr Bratton's relevance in an interview with told the Independent on Sunday.
"If you look at the style of policing in the States, and their levels of violence, they are fundamentally different from here," he said.
"What I suggested to the home secretary is a more sensible approach, maybe to look across far wider styles of policing and - more usefully - at European styles; they, like us, are bound by the European Convention.
"My sense is, when we've done that, we will find the British model is probably the top."
Home Secretary Theresa May said Mr Bratton was to be consulted as part of a process of learning from people around the world who had experience of tackling gang culture.
"I'm going to be listening to people internationally - yes, from America, but from other parts of the world where they've been dealing with gangs - and also let's recognise the good work that's been done in the UK," Mrs May said.
'Inconsistency of guidance'
There has been friction between ministers and senior police in the aftermath of last week's nights of rioting.
Mr Cameron has suggested police were too timid, and with too few officers on the ground, in their early efforts to tackle the riots.
Senior officers rejected that claim, and have also clashed with government over whether police or ministers planned the surge in officer numbers on Tuesday that put an end to widespread violence in the capital.
Acting Metropolitan Police Commissioner Tim Godwin accused Parliament of offering "inconsistency of guidance" related to tackling public disorder.
"We sometimes are accused of excessive force and then we're accused of not being forceful enough," Mr Godwin said.
Since order was restored to the streets, there has also been a growing debate about anticipated reductions in police numbers as part of budget cuts.
Mr Godwin warned that policing of any future similar disturbances would be made even harder.
Labour's shadow policing minister Vernon Coaker said: "Tactics could only change when they had enough police, and the surge of numbers that we saw - that have brought the streets back under control in London as quickly as possible - could only take place once those numbers of police had been mobilised."
He added: "I think it proves that numbers of police count."
Chancellor George Osborne has dismissed calls to reverse cuts to police budgets in the wake of last week's violence.
Mrs May said: "It is possible to make cuts in police budgets without affecting their ability to do the job the public want them to do and ensuring the police can still provide front-line services."
Forces would have to move officers "out from their desks and out there on the streets", she said.
Before the courts
But Conservative London mayor Boris Johnson said there was "going to have to be an argument about money".
"The case I make to the government, and I'm going to continue to make, is that numbers matter," he told Sky News.
"What Londoners want to see now is loads of police out there on the streets - that's what's been successful over the last few days. That's the policy people want us to keep up with."
In other developments related to last week's trouble in London, the East and West Midlands, Manchester, Liverpool and Gloucester:
- The killers of a man shot dead in Croydon, south London, on Monday are believed to have been involved in looting, detectives have said. Three men have been arrested over the murder of 26-year-old Trevor Ellis
- A 33-year-old man has become the fourth person arrested in connection with a fire that destroyed the family-run Reeves Furniture store during the violence in Croydon
- Scotland Yard revealed that 1,401 people had now been arrested in connection with the unrest, and 808 charged. The force has released a further 44 images of suspects thought to be involved in rioting
Mr Godwin predicted that a total of about 3,000 people could eventually be brought before the courts in relation to the violence in London.
"That's yet to be worked through but we have lots and lots of images, we have lots and lots of CCTV and there were lots of people involved," he said.
Writing in the Observer, Liberal Democrat deputy leader Simon Hughes warned against "knee-jerk solutions" in the wake of last week's riots.
As many Conservatives back plans to cut benefits and evict families of rioters from their homes, Mr Hughes warned such moves could "have the reverse effect to that intended".
The Bishop of Manchester, the Right Reverend Nigel McCulloch, has called for a return to moral values where respect for others is placed above possessions.
In a sermon for BBC Radio 4's Sunday Worship programme, Bishop McCulloch condemned "a me-first, ultra-consumerist culture, in which the quest for possession of things overrides a caring concern for others, and the key commandments become don't get caught and don't grass".
"This week we've had an unpleasant glimpse of the default position to which society inevitably returns when its moral imperatives are forgotten," he said.
On a visit to Manchester on Saturday, Deputy Prime Minister Nick Clegg played down any dispute between the government and the police.
"There is no rift... we fully support the police 100%," he said.
"They have done a brilliant job in really difficult circumstances. The police themselves have said they want to review what happened and look at tactics and learn lessons."
In a statement, Downing Street said Mr Bratton had long-standing links with British policing and they thanked him for agreeing "to make himself available for a series of meetings in the UK in the autumn to share his experience of tackling gangs".
Mr Bratton - credited with restoring law and order in Los Angeles after riots in 1992 - said: "You can't arrest your way out of the problem.
"Arrest is certainly appropriate for the most violent, the incorrigible, but so much of it can be addressed in other ways and it's not just a police issue, it is in fact a societal issue."